We're missing some context that probably says that there is some kind of dispute about the way in which this school decides who it will admit. Clearly it is a school that parents wish their children to attend.
It seems that the dispute involves people in the area who are not the local gentry and professional classes.
... the local gentry and professional classes had held aloof ...
They had kept themselves out of the dispute, not involved, distant from it.
... for the school had accepted their sons readily enough.
Because whatever the school was doing in relation to other children, it was not causing them any problems.